The paper studies a system of Hamilton-Jacobi equations, arising from a stochastic optimal debt management problem in an infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool of risk-neutral lenders. In this model, the borrower is a sovereign state that can decide how much to devaluate its currency and which fraction of its income should be used to repay the debt. Moreover, the borrower has the possibility of going bankrupt at a random time and must declare bankruptcy if the debt reaches a threshold x*. When bankruptcy occurs, the lenders only recover a fraction of their capital. To offset the possible loss of part of their investment, the lenders buy bonds at a discounted price which is not given a priori. This leads to a nonstandard optimal control problem. We establish an existence result of solutions to this system and in turn recover optimal feedback payment strategy u*(x) and currency devaluation v*(x). In addition, the behavior of (u*,v*) near 0 and x* is studied.

A Model of Debt with Bankruptcy Risk and Currency Devaluation

Rossana Capuani;
2020

Abstract

The paper studies a system of Hamilton-Jacobi equations, arising from a stochastic optimal debt management problem in an infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool of risk-neutral lenders. In this model, the borrower is a sovereign state that can decide how much to devaluate its currency and which fraction of its income should be used to repay the debt. Moreover, the borrower has the possibility of going bankrupt at a random time and must declare bankruptcy if the debt reaches a threshold x*. When bankruptcy occurs, the lenders only recover a fraction of their capital. To offset the possible loss of part of their investment, the lenders buy bonds at a discounted price which is not given a priori. This leads to a nonstandard optimal control problem. We establish an existence result of solutions to this system and in turn recover optimal feedback payment strategy u*(x) and currency devaluation v*(x). In addition, the behavior of (u*,v*) near 0 and x* is studied.
Debt management and bankruptcy
optimal feedback solution
stochastic optimal control
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1041819
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact